An NMF Perspective on Binary Hashing

Binary Hashing with Semidefinite Relaxation and Augmented Lagrangian

“…where S v and Z v are vector forms of S and Z, respectively; M is a constant binary matrix; I is identity matrix; ⊗ is Kronecker product [11]. The differences between our AL, SDR approaches and two above approaches of [11] are quite clear.…”

“…Our work is inspired by a few recent supervised hashing methods [15,16] and unsupervised hashing method [11] which rely on two-step approach to reduce the complexity of the coupled problem and to make the flexibility in using of different types of hash functions. In particular, those works decompose the learning of hash functions under binary constraint into two steps: the binary code inference step and the hash function learning step.…”

“…After getting the binary codes, the hash function learning step becomes a classical binary classifier learning. Hence, it allows the using of various types of hash functions, i.e., linear SVM [11], kernel SVM [15], decision tree [16].…”

“…In [11], the authors solve the binary code inference using non-linear optimization approach or non-negative matrix factorization approach. We will brief the approaches in [15,16,11] when comparing to our methods in section 2.4.…”

“…Although different methods are proposed for inferencing the binary code, the disadvantage of those methods [15,11] is that in order to overcome the hardness of the binary constraint on codes, they solve the relaxed problem, i.e., relaxing the binary constraint to continuous constraint. This may decrease the code quality and incurs some performance penalty.…”